Claire, age 16, told us that the answer was 9 (which is right), but she didn't tell us how she worked it out.

Sally showed us her workings (she told us she used the hint!).

1 1+Ö2

+

1 Ö2+Ö3

+

1 Ö3+Ö4

+ ¼+

1   __ Ö99   +   ___ Ö100

=

1-Ö2 1-2

+

Ö2-Ö3 2-3

+

Ö3-Ö4 3-4

+¼+

__ Ö99   -   ___ Ö100   99-100

(multiplying top and bottom of each fraction).
So the sum is

-

æ è

1-Ö2+Ö2-Ö3+Ö3-Ö4+¼+

__ Ö99

-

___ Ö100

ö ø

=-(1-10)=9

.